| John Bonnycastle - Algebra - 1811 - 220 pages
...III. The last term of any arithmetical series is equal to the sum or difference of the first term, and **the product of the common difference by the number of terms less , one** ; according as the series is increasing or decreasing. Thus, the 20th term of 2, 4, 6, 8, 10, 12, &c.... | |
| John Bonnycastle - Algebra - 1813
...2 x (a+2d). 5. The last term of any increasing arithmetical series is equal to the first term plus **the product of the common difference by the number of terms less one** ; and if the series be decreasing, it will he equal to the first term minus that product. Thus, the... | |
| John Bonnycastle - Algebra - 1818 - 260 pages
...Or, the sum of any increasing arithmetical series may be found, without considering the last term, **by adding the product of the common difference by the number of terms less one to** twice the first term, and then multiplying the result by half the number of terms. And, if the series... | |
| John Bonnycastle - Algebra - 1818 - 260 pages
...(a+4d)=(a+d)+(a+3d)=2 X(o+2«i). 5. The last term of any increasing arithmetical series is equal to the first term plus **the product of the common difference by the number of terms less one** ; and if the series be decreasing, it will be equal to the first term minus that product. Thus, the... | |
| Thomas Keith - Arithmetic - 1822 - 332 pages
...13- &c- be 'n arithmetical progression, then will 4. The difference between the extremes is equal to **the product of the common difference by the number of terms less one>** Thus, if 3. 5. 7. 9. &c. be in arithmetical progression, Tlien will 9—3=2x4—15. The number of terms,... | |
| Enoch Lewis - Arithmetic - 1824
...subsequent term, it is manifest that the whole sum, by which the first term is increased or diminished, is **the product of the common difference by the number of terms less one.** (48.) The sum of the extremes is evidently equal to the sum of the second from thebeginning, and the... | |
| James Ryan - Algebra - 1824 - 516 pages
...the terms. Hence the last term of any arithmetical series is equal to the. first term plus or minus, **the product of the common difference, by the number of terms less one.** 469. Also, if s be put equal to the sum of any number of terms of this progression, we shall have And... | |
| James Ryan - Algebra - 1824 - 516 pages
...the terms. Hence the last term of any arithmetical series is equal to the first term plus or minus, **the product of the common difference, by the number of terms less one.** 469. Also, if s be put equal to the sum of any number of terms of this progression, we shaU have And... | |
| John Bonnycastle - Algebra - 1825 - 312 pages
...-:d)= x (a+td.) 5. The last term of any increasing arithmetical series is equal to the first term plus **the product of the common difference by the number of terms less one** ; and it ^ the series be decreasing, it will be equal to the first term minus that product. Thus, the... | |
| Warren Colburn - Algebra - 1828 - 276 pages
...term, r the common difference, and n the number of terms. The series is «, a -f- r, a -f- 2 r, a -f- **3 r . . . . a -f- (n — 2) r, a -\- (n — 1) r....series 3, 5, 7, 9, &c. In this a = 3, r = 2, and n** — 1 =9. 1 = 3 + 9 X2 = 21. In a decreasing series, r is negative. .? Example. What is the 13th term... | |
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